written 6.5 years ago by | modified 6.4 years ago by |
• In a small signal model, we can take a nonlinear circuit or device and make approximations which linearize it about an DC operating point.
• To do this, we write all voltages and currents as the sum of a DC value for each, plus a small extra amount which is the small signal.
• Consider the above circuit,
Input voltage is vD(t)=VD+vd(t)
• DC analysis: The purpose of DC analysis is to find the operating point of diode. To do DC analysis, turn off the small AC signal
The voltage vD(t)=VDvD(t)=VD
And the current iD(t)=ID=ISexp(VDηvT)
• When small AC signal is applied
Total Voltage across diode is vD(t)=VD+vd(t)vD(t)=VD+vd(t)
Total instantaneous current is iD(t)=ISexp(VD+vd(t)ηvT)iD(t)=ISexp(VD+vd(t)ηvT)
iD(t)=ISexp(VDηvT)×exp(vd(t)ηvT)iD(t)=ISexp(VDηvT)×exp(vd(t)ηvT)
iD(t)=ID×exp(vd(t)ηvT)iD(t)=ID×exp(vd(t)ηvT)
When vd(t)<<ηvTvd(t)<<ηvT hence (vd(t)ηvT<<1)(vd(t)ηvT<<1) therefore we can ignore powers of vd(t)ηvTvd(t)ηvT
expvd(t)ηvT)≈1+vd(t)ηvTexpvd(t)ηvT)≈1+vd(t)ηvT
iD(t)≈ID(1+vd(t)ηvT)iD(t)≈ID(1+vd(t)ηvT)
iD(t)≈ID+IDηvTvd(t)iD(t)≈ID+IDηvTvd(t)
iD(t)=ID+id(t)iD(t)=ID+id(t)
id(t)=IDηvTvd(t)id(t)=IDηvTvd(t)
Since IDηvT is a ratio of current and voltage hence we can replace it by resistance
Inverse of IDηvT=ηvTID=rdIDηvT=ηvTID=rd
• Small signal AC equivalent circuit is